Bode plots & margins worksheet with answers

Free printable Bode plots & margins worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
|H| (dB)0.1110100100002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 3600(s + 1)/((s + 40)(s + 8)) in decibels, |G(0)| in dB.

G(s) = 3600(s + 1)/((s + 40)(s + 8))
|G(0)| = dB
2.Easy
|H| (dB)1101001000−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 20/(s(s + 20)). What is the slope n of the straight-line asymptote above 20 rad/s, in dB/decade?

G(s) = 20/(s(s + 20))
n = dB/dec
3.Medium
|H| (dB)0.11101001000−60−40−20020ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 2223/((s + 13)(s + 19)) at ω = 8 rad/s, in dB.

G(s) = 2223/((s + 13)(s + 19))ω = 8 rad/s
|G(jω)| = dB
4.Medium
vin​R = 4.7 kΩC = 22 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 22 nF. A sinusoidal input of 4.6 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 22 nFf = 4.6 kHz
|H| = dB
5.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = 244/(s(s + 4)(s + 7)). Find the gain margin GM in dB.

L(s) = 244/(s(s + 4)(s + 7))
GM = dB
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = K/(s(s + 3)(s + 6)). Find the gain K that gives a gain margin of 5 dB.

L(s) = K/(s(s + 3)(s + 6))GM = 5 dB
K =

Answer key

  1. 1. |G(0)| = 21.02 dB
  2. 2. n = −40 dB/dec
  3. 3. |G(jω)| = 16.98 dB
  4. 4. |H| = −9.97 dB
  5. 5. GM = 2.023 dB
  6. 6. K = 91.1

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